Method for active noise cancellation using independent component analysis

ABSTRACT

The present invention considers a method for active cancellation using independent component analysis. More particularly, the present invention relates to a method which is operable the independent component analysis technique to an adaptive algorithm that can consider secondary or more higher statistical characteristics.  
     The conventional active noise cancellation systems mainly use the LMS(Least Mean Square) which considers secondary statistics among input signals.  
     Being different from the conventional active noise cancellation systems, the present invention provides a method for active noise cancellation using independent component analysis, which makes output signals independent of each other by considering secondary or more higher statistical characteristics.  
     Therefore, according to the present invention, the improved performances of the noise cancellation systems can be provided compared with the conventional active noise cancellation system which uses the LMS adaptive algorithm.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention considers a method for active noisecancellation using independent component analysis. More particularly,the present invention relates to a method which is operable theindependent component analysis technique to an adaptive algorithm thatcan consider secondary or more higher statistical characteristics.

[0003] 2. Description of the Related Art

[0004]FIG. 1 shows a structure of a general active noise cancellationsystem. In FIG. 1, a signal source(10) s is transmitted to a sensorthrough a channel, and a noise source(20) n₀ is input in the sensor sothat the combined signal and noise s+n₀ form primary input(30) in thenoise cancellation system.

[0005] The secondary sensor receives noise n₁ through another channel,and the sensor forms reference input(40) in the noise cancellationsystem. The noise n₁ is filtered to produce an output z, which is asclose as possible of n₀, by passing through an adaptive filter(50), andthe primary input s+n₀ deducts output z through an adder(60) and formssystem output(70) u=s+n₀−z in the noise cancellation system.

[0006] The purpose of the conventional active noise cancellation is toget output u=s+n₀−z which is as close as possible of signal s in thepoint of least squares. To reach the purpose, the filter is adaptedusing a least mean square(LMS) adaptive algorithm to minimize the entireoutput of the noise cancellation system. In other words, the output inthe active noise cancellation system is operated as an error signalduring adaptation.

[0007] The coefficient adaptation of the filter follows the Widrow-HoffLMS algorithm and can be expressed as following expression.

[0008] Expression 1

Δw(k)αu(t)n ₁(t−k)

[0009] Where, w(k) is k^(th) order coefficient, and t is sample index.

SUMMARY OF THE INVENTION

[0010] The purpose of the present invention is to provide a method foractive noise cancellation using independent component analysis, whichallows to get the improved performances of the noise cancellationsystems compared with the conventional LMS adaptive algorithm.

[0011] To reach the said purpose of the present invention, beingdifferent from the conventional noise cancellation systems, the presentinvention provides a method for active noise cancellation usingindependent component analysis, which makes output signals independentof each other by considering secondary or more higher statisticalcharacteristics.

BRIEF DESCRIPTION OF DRAWINGS

[0012]FIG. 1 shows a structure of a general active noise cancellationsystem.

[0013]FIG. 2 shows a structure of a feedback filter according to thepresent invention.

[0014]FIG. 3 shows a structure of a feedback filter for active noisecancellation according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] Hereafter, an embodiment according to the present invention isdescribed in detail by referring to accompanying drawings.

[0016]FIG. 2 shows a structure of a feedback filter according to thepresent invention, and FIG. 3 shows a structure of a feedback filter foractive noise cancellation according to the present invention.

[0017] Independent component analysis can recover unobserved independentsource signals from the combined signals of sound sources which aremixed through an unknown channel. Let us consider a set of unknownsources, s(t)=[s₁(t), s₂(t), . . . , s_(N)(t)]^(T), such that thecomponents s_(i)(t) are zero-mean and mutually independent. From Nsensors, it is obtained a set of signals, x(t)=[x₁(t), x₂(t), . . . ,x_(N)(t)]^(T), which are mixed through a channel from the sources,s(t)=[s₁(t) , s₂(t) , . . . , s_(N)(t)]^(T). If a channel can be modeledas instantaneous mixing, the sensor signals, x(t)=[x₁(t), x₂ (t), . . ., x_(N)(t)]^(T), can be expressed as following expression.

[0018] Expression 2

x(t)=A·s(t)

[0019] Where, A is an unknown invertable matrix called as a mixingmatrix.

[0020] Therefore, it is the subject to retrieve the sound sources byfinding the inverse matrix of the mixing matrix A using only sensorsignals x(t).

[0021] However, recovering a permuted and rescaled version of originalsound sources doesn't matter from the standpoint of source separationbecause it doesn't affect their waveforms.

[0022] Therefore, by estimating the unmixing matrix W, the retrievedsignals u(t), which are the original ones up to permutation and scaling,is acquired from the following expression.

[0023] Expression 3

u(t)=W·x(t)

[0024] Herein, to estimate the unmixing matrix W, it is assumed thateach of sound sources is independent. It means that a signal from onesound source doesn't affect a signal from another source, and it can beconsidered as possible suppose. Also, the statistical independenceincludes the statistical characteristics of all orders.

[0025] Because the statistical independence doesn't affect permutationand scaling, the unmixing matrix W of expression 3 can be obtained. Theunmixing matrix W is learned by using the following expression whichmakes the statistical independence among estimated source signalsmaximize.

[0026] Expression 4${{\Delta \quad W} \propto {\left\lbrack W^{T} \right\rbrack^{- 1} - {{\phi (u)}x^{T}}}},{{\phi \left( {u_{i}(t)} \right)} = {- \frac{\frac{\partial{P\left( {u_{i}(t)} \right)}}{\partial{u_{i}(t)}}}{P\left( {u_{i}(t)} \right)}}}$

[0027] Where, P(u_(i)(t)) approximates the probability density functionof estimated source signal u_(i)(t).

[0028] In real world situations, instantaneous mixing is hardlyencountered, and the mixing of sources involves convolution andtime-delays as following expression.

[0029] Expression 5${x_{1}(t)} = {\sum\limits_{j = 1}^{N}\quad {\sum\limits_{k = 0}^{K - 1}\quad {{a_{ij}(k)}{s_{j}\left( {t - k} \right)}}}}$

[0030] Where, x₁(t) is a measured sensor signal, s_(j)(t) is a soundsource signal, and a_(ij)(k) is a coefficient of a mixing filter oflength K.

[0031] To separate the source signals, the feedback filter structure ofFIG. 2 can be used. Where, the recovered signal u_(i)(t) can beexpressed as following.

[0032] Expression 6${u_{i}(t)} = {{\sum\limits_{k = 0}^{K}\quad {{w_{ij}(k)}{x_{1}\left( {t - k} \right)}}} + {\sum\limits_{j = {{1j} \neq i}}^{N}\quad {\sum\limits_{k = 1}^{K}\quad {{w_{ij}(k)}{u_{j}\left( {t - k} \right)}}}}}$

[0033] Where, w_(ij)(k) shows k^(th) order coefficient of the filter toestimate an original sound sources.

[0034] In this structure, there are three different cases of the filtercoefficients. In other words, these are w_(ii)(0) which is a zero delaycoefficient in a direct filter, w_(ii)(k), k≠0 which is a delaycoefficient in a direct filter, and w_(ij)(k), i≠j which is acoefficient in a feedback cross filter. Learning rules for all thesecases are as following.

[0035] Expression 7$\quad {{{\Delta \quad {w_{ii}(O)}} \propto {{1/{w_{ii}(O)}} - {{\phi \left( {u_{i}(t)} \right)}{x_{i}(t)}}}},{{\Delta \quad {w_{ii}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{x_{i}\left( {t - k} \right)}}},{{\Delta \quad {w_{ij}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{u_{j}\left( {t - k} \right)}}},{{\phi \left( {u_{i}(t)} \right)} = {- \frac{\frac{\partial{P\left( {u_{i}(t)} \right)}}{\partial{u_{i}(t)}}}{P\left( {u_{i}(t)} \right)}}}}$

[0036] Zero delay coefficient, w_(ii)(0) , scales the data to maximizethe information transmitted through the nonlinear function, delaycoefficient, w_(ii)(k), k≠0, whitens each output from the correspondinginput signal temporally, and coefficient in a feedback cross filter,w_(ij)(k), i≠j, decorrelates each output φ(u_(j)(t)) from all otherrecovered signal u_(j)(t).

[0037]FIG. 2 shows the feedback filter structure with two inputs andoutputs. However, by increasing the number of inputs and outputs in thefeedback filter structure, a feedback filter structure can beconstructed with an arbitrary number of inputs and outputs. And, in thisstructure, the same expressions as expression 5, 6, and 7 that show themixed signals, recovered signals, and learning rules of filtercoefficients can be used.

[0038] For the convolved mixtures, the recovered signals are thewhitened origin source signals temporally. Therefore, whitening problemcan be solved by remaining zero delay coefficient, w_(ii)(0), and fixingdelay coefficient, w_(ii)(k), k≠0.

[0039] In case that pure noise can be observed, noise component frommixed signal can be canceled by using independent component analysis.

[0040] In FIG. 1, which shows basic active noise cancellation, it can beassumed that noise n₁ and signal s are independent to each other, butnoise n₁ is related to noise n₀ in unknown way. Because signal and noisedo not affect each other, this assumption is reasonable.

[0041] Independent component analysis can be used to cancel noisedependent component of primary input by the secondary input. The primaryinput is the mixed signal of noise and signal, and the secondary inputis noise component without signal component, therefore, the feedbackfilter structure for independent component analysis can be modified.

[0042] In other words, when the primary and secondary input are x₁ andx₂ respectively like in FIG. 2, the secondary input x₂ is the noisecomponent without signal component, so it is not required feedbackfilter W₂₁(k) of expression 6.

[0043] The feedback filter structure, which has two inputs and outputsthat do not use feedback filter W₂₁(k) , is shown as the structure ofFIG. 3 and can be expressed as following expression.

[0044] Expression 8${{u_{1}(t)} = {{\sum\limits_{k = 0}^{K}\quad {{w_{11}(k)}{x_{1}\left( {t - k} \right)}}} + {\sum\limits_{k = 1}^{K}\quad {{w_{12}(k)}{u_{2}\left( {t - k} \right)}}}}},{{u_{2}(t)} = {\sum\limits_{k = 0}^{K}\quad {{w_{22}(k)}{x_{2}\left( {t - k} \right)}}}}$

[0045] By comparing FIG. 1 which shows basic active noise cancellationsystem and FIG. 3, the mixture s+n₀ of signal and noise, which forms theprimary input, is corresponding to x₁, whereas n₁, which forms thesecondary input, is corresponding to x₂. Also, output u is correspondingto u₁.

[0046] Herein, in case of remaining zero delay coefficient, w_(ii)(0),and fixing delay coefficient, w_(ii)(k), k≠0to 0, because feedbackfilter w₂₁(k) is not used, output signal u₁ of expression 8corresponding to output u of the conventional active noise cancellationsystem can be expressed using two inputs x₁ and x₂ as following.

[0047] Expression 9${u_{1}(t)} = \quad {{{w_{11}(O)}{x_{1}(t)}} + {{w_{22}(O)}{\sum\limits_{k = 1}^{K}\quad {{w_{12}(k)}{x_{2}\left( {t - k} \right)}}}}}$

[0048] The second term of the expression 9 corresponds to output z ofthe adaptive filter in the conventional active noise cancellationsystem. Therefore, the feedback filter structure of independentcomponent analysis for active noise cancellation can be considered asthe same structure of the conventional active noise cancellation system.

[0049] The learning rule of each filter coefficient for an active noisecancellation system can be expressed by independent component analysisas following.

[0050] Expression 10$\quad {{{\Delta \quad {w_{ii}(O)}} \propto {{1/{w_{ii}(O)}} - {{\phi \left( {u_{i}(t)} \right)}{x_{i}(t)}}}},{{\Delta \quad {w_{ii}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{x_{i}\left( {t - k} \right)}}},{{\Delta \quad {w_{ij}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{u_{j}\left( {t - k} \right)}}},{{\phi \left( {u_{i}(t)} \right)} = {- \frac{\frac{\partial{P\left( {u_{i}(t)} \right)}}{\partial{u_{i}(t)}}}{P\left( {u_{i}(t)} \right)}}}}$

[0051] Output of the active noise cancellation system obtained bylearning filter coefficients is signal component which is independent ofnoise component.

[0052] In FIG. 3, the feedback filter structure for active noisecancellation with two inputs and outputs can be extended to an structurewith arbitrary number of inputs and outputs like in FIG. 2, and therecovered signals and learning rules of coefficients in the saidfeedback filter structure for active noise cancellation which hasarbitrary number of inputs and outputs can be obtained by extendingexpression 8 and 10 in the same way.

[0053] As mentioned above, the method for active noise cancellationusing independent component analysis according to the present inventionprovides the improved noise cancellation performances compared withthose of the active noise cancellation system which uses theconventional LMS adaptive algorithm.

What is claimed is:
 1. A method for active noise cancellation usingindependent component analysis which is characterized by adaptation of afilter to get components among signal components of the primary inputwhich are independent of noise components which form the secondary inputat the output end in active noise cancellation system, wherein themixture of signal and noise that forms the primary input and noise thatforms the secondary input.
 2. The method for active noise cancellationusing independent component analysis according to claim 1, whereinsignal cancellation range corresponding to active noise is extended forthe system which acquires many noise signals or mixtures of signal andnoise by increasing the number of inputs or outputs of the said activenoise cancellation system.
 3. The method for active noise cancellationusing independent component analysis which is characterized by cancelingactive noise by including the following steps or an arbitrary step; in acancellation method of active noise cancellation system with a feedbackstructure, (a) wherein zero delay coefficient, w_(ii)(0), scales thedata to maximize the information transmitted through the nonlinearfunction, (b) wherein delay coefficient, w_(ii)(k), k≠0, whitens eachoutput from the corresponding input signal temporally, and (c) whereincoefficient in a feedback cross filter, w_(ij)(k), i≠j, decorrelateseach output${{\phi \left( {u_{i}(t)} \right)} = {{- \frac{\frac{\partial{P\left( {u_{i}(t)} \right)}}{\partial{u_{i}(t)}}}{P\left( {u_{i}(t)} \right)}}\quad {from}\quad {all}\quad {other}\quad {recovered}\quad {signal}\quad {u_{j}(t)}}},$

where the said P(u_(i)(t)) approximates the probability density functionof estimated source signal u_(i)(t).
 4. The method for active noisecancellation using independent component analysis according to claim 3,wherein signal cancellation range corresponding to active noise isextended for the system which acquires many noise signals or mixtures ofsignal and noise by increasing the number of inputs or outputs of thesaid active noise cancellation system.
 5. The method for active noisecancellation using independent component analysis which is characterizedby controlling active noise by learning each adaptive filter coefficientaccording to the following expression in active noise cancellationsystem, wherein the mixture x₁ of signal and noise that forms theprimary input and noise x₂ that forms the secondary input. Expression 11$\quad {{{\Delta \quad {w_{ii}(O)}} \propto {{1/{w_{ii}(O)}} - {{\phi \left( {u_{i}(t)} \right)}{x_{i}(t)}}}},{{\Delta \quad {w_{ii}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{x_{i}\left( {t - k} \right)}}},{{\Delta \quad {w_{ij}(k)}} \propto {{- {\phi \left( {u_{i}(t)} \right)}}{u_{j}\left( {t - k} \right)}}},{{\phi \left( {u_{i}(t)} \right)} = {- \frac{\frac{\partial{P\left( {u_{i}(t)} \right)}}{\partial{u_{i}(t)}}}{P\left( {u_{i}(t)} \right)}}}}$

herein, the said w_(i1)(0) is a zero delay coefficient in a directfilter, w_(i1)(k), k≠0 is a delay coefficient in a direct filter,w_(ij)(k), i≠j is a coefficient in a feedback cross filter, Δ before ofeach coefficient is change amount of the corresponding coefficient, t issample index, and P(u_(i)(t)) approximates the probability densityfunction of estimated source signal u_(i)(t).
 6. The method for activenoise cancellation using independent component analysis according toclaim 5, which is characterized by obtaining the said u_(i)(t) byfollowing expression. Expression 12${{u_{1}(t)} = {{\sum\limits_{k = 0}^{K}\quad {{w_{11}(k)}{x_{1}\left( {t - k} \right)}}} + {\sum\limits_{k = 1}^{K}\quad {{w_{12}(k)}{u_{2}\left( {t - k} \right)}}}}},{{u_{2}(t)} = {\sum\limits_{k = 0}^{K}\quad {{w_{22}(k)}{{x_{2}\left( {t - k} \right)}.}}}}$


7. The method for active noise cancellation using independent componentanalysis according to claim 5, wherein signal cancellation rangecorresponding to active noise is extended for the system which acquiresmany noise signals or mixtures of signal and noise by increasing thenumber of inputs or outputs of the said active noise cancellationsystem.